Question

Match the function with its graph.

Answer 1

I am confused because:

g(x) = x^5-3x^2+1, a <0 makes the graph of choice 3
g (x) = x^3-3x^2+1, a>0 makes the graph of choice 3

f (x) = x^4-3x^2+1, a>0 makes the graph of choice 1
f (x) = x^6-3x^2+1, a<0 makes the graph of choice 1

Choices 1 and 3 look like it would go to + infinity
Choices 2 and 4 look like it would go to - infinity

Answer 2

so let's look at graph 1...
it looks like from what you said above you know you must have an even degree polynomial
correct?

Answer 3

yeah

Answer 4

ok great so we have the options g(x)=ax^4 where a>0
or g(x)=ax^6 where a<0
as are only options

Answer 5

for the first graph

Answer 6

the trick is the negative and positive part

Answer 7

do you know what g(x)=x^4 and g(x)=-x^6 look like?

Answer 8

or at least their end behavior

Answer 9

I graphed it where does the g(x)=-x^6 come from the - sign?

Answer 10

I'm going to call them something different...
g(x)=x^4
and
f(x)=-x^6
---

g(100)=100^4 <--a really really big positive number
where as
f(100)=-100^6 <---a really really big negative number

Answer 11

your options says a<0

Answer 12

for the x^6 graph

Answer 13

a<0 means a is negative

Answer 14

a>0 means a is positive

Answer 15

oh I see > greater than which is + and < less than which is -

Answer 16

yep
and I just chose 1 and -1 because they are the prettiest negative and positive numbers

Answer 17

f(x)=1x^4 and g(x)=-1x^6

look at graphs 1 and 4...
which graph would be closer to something like f(x)=1x^4?

Answer 18

like just look at the end behavior
or look at what f(100)=100^4 this means when you plug in a really large positive x value you are going to get a really ridiculous large positive output y value

Answer 19

graph 4 says well if I plug in a really big positive x value I'm going to get a really big negative y output

Answer 20

I got it now from top to bottom would be

2
1
4
3

the - in front of the x's was where I was making a mistake.

Answer 21

you got it

Answer 22

Thank you for taking the time to explain this to me I really appreciate it :)

Answer 23

np :)